Can magnetic field expand faster than light?

[Mapes]

If the change is fast enough, it produces a wave capable of self propagating - EM wave.

There is no speed requirement. Any change in electric or magnetic field, no matter how slow, propagates as an EM signal with speed c (with a very long wavelength).

 

[Tominator]

yes i understand how waves are made, but not what they actually are made of. eg, a wave in the sea is made of water, or water is what propagates the wave energy. i suppose what I'm getting at, is what is the physical property of EM waves, or are they made of nothing?

The nature of every wave is energy. The EM waves are made of energy as well. The water waves needs water as environment to propagate, but again, they are nothing else than energy. It is said that EM waves does not need any environment to propagate. But on the first page of this forum DaveC said that electric and magnetic field extend to infinity. So then the environment, in which EM waves propagate would be everywhere. But EM waves are not like the water waves, they are composed of photons. Photon is something between wave and particle. But I still do not understand it so well to teach you, there are better explanations of EM waves all around the forum, you only need to do a bit of searching.

There is no speed requirement. Any change in electric or magnetic field, no matter how slow, propagates as an EM signal with speed c (with a very long wavelength).

I have heard, that EM waves with frequency under 50Hz are considered oscilations of the field.

 

[Mapes]

Never heard of a cutoff at 50 Hz. Can you provide a reference so's I might learn more?

 

[Tominator]

Never heard of a cutoff at 50 Hz. Can you provide a reference so's I might learn more?

By " I have heard " I really meant heard, so sorry but I can't provide you with any references. I meant it more as a question, because I was not and I am not sure about it. But it is something I have heard at school, so I expected it to be right. Maybe my memory messed it up somehow with the equation of progressive Em wave. You might post a new thread with this question if you want.

 

[Dale]

dalespam. I've got news for you. Your statement
"The magnitude of the momentum of light is given by p = E/c, so it is independent of the frequency"
Wrong, wrong ! E = hf. Energy of a photon is directly proportional to frequency.

I am not wrong, but I guess I should have been more clear. I was thinking specifically in terms of a space propulsion system. So if you have a vehicle that carries a finite quantity of fuel then your E is fixed. Assuming that you could convert your fuel to light of two different frequencies, then for the lower frequency you would generate more photons of lower energy each than for the higher frequency. The total momentum of all the photons would be the same at both frequencies.

 

[Tominator]

Hmmm
But isn't the light propulsion extremely inefficient? Because if you compare the energy (power) used to "throw off" light, to the momentum gained, it looks to me that it is extremely inefficient. If you use the same energy to push off a magnet by electromagnet, the momentum gained is far more greater.

 

[Dale]

I already answered that several times Tominator.

 

[Tominator]

I already answered that several times Tominator.

Yes sorry, I only wanted to take it step by step, as you have suggested.
Well, if something is inefficient, but working, there is always possibility to make it work as efficiently, as technology will let us. Because waves are actually energy, the light propulsion is gaining momentum directly by "throwing off" energy. That seemingly violates the law of conservation of momentum, but as far as I know, law of conservation of energy is superior to law of conservation of momentum.
doesnt the law of conservation of momentum apply only on closed systems? (no energy out or in)
If my assumptions are correct, than it is not a physical non-sense to run around the law of conservation of momentum, by using non-closed system and law of conservation of energy. Thus creating propulsion system, capable of creating force in one direction directly from energy. (?)

 

[Klockan3]

Hmmm
But isn't the light propulsion extremely inefficient? Because if you compare the energy (power) used to "throw off" light, to the momentum gained, it looks to me that it is extremely inefficient. If you use the same energy to push off a magnet by electromagnet, the momentum gained is far more greater.

Actually light is the by far most efficient thing to throw off.

First you know the formula E=mc^2, right? It means that energy=mass.
Then you also got from special relativity that mass is just energy with its momentum vector along the time axis, and that energy is the length of these momentum vectors, and that no matter the direction the object always move in it with the speed of c. Of course we use the general coordinates of ct being the time axis.

Then you see that you get the most momentum per energy by using pure light, since it got no mass which gives 0 momentum per energy and everything in between light and mass is just a mix.

Anyway the reason we don't propagate things using light is because we aren't that good at transforming mass to energy.


Anyway, your thing about electomagnets, the problem with your analysis is that when you look at electro magnets strength you look at stable fields. Stable fields never give out any momentum, its just oscillating fields. Oscillating magnet fields becomes electro magnetic radiation in the same way oscillating electric fields creates electro magnetic radiation, they are the same phenomenon.

If you want to compare anything you should compare the magnetic field with the electric field, and then the magnetic field is weaker unless you move at the speed of light in which case they are equal. The only reason you notice magnetic fields more is because a wire can have charges move relative to each other while still have a total charge of 0 meaning that you get magnetic fields without electric fields, however if you would isolate just a few grams of purely charged matter you would get extreme forces.

 

[Dale]

Because waves are actually energy, the light propulsion is gaining momentum directly by "throwing off" energy. That seemingly violates the law of conservation of momentum, but as far as I know, law of conservation of energy is superior to law of conservation of momentum.

No, conservation of energy and conservation of momentum are on equal footing. They are the timelike and spacelike parts of the http://en.wikipedia.org/wiki/Four-momentum#Conservation_of_four-momentum" respectively. This is what Klockan3 is referring to in his second paragraph.

doesnt the law of conservation of momentum apply only on closed systems? (no energy out or in)

Yes, same with the conservation of energy.

If my assumptions are correct, than it is not a physical non-sense to run around the law of conservation of momentum, by using non-closed system and law of conservation of energy. Thus creating propulsion system, capable of creating force in one direction directly from energy. (?)

You cannot run around either conservation law. All you can do is understand them and use them to accomplish your design goal. TANSTAAFL

 

[Tominator]

Anyway, your thing about electomagnets, the problem with your analysis is that when you look at electro magnets strength you look at stable fields. Stable fields never give out any momentum, its just oscillating fields. Oscillating magnet fields becomes electro magnetic radiation in the same way oscillating electric fields creates electro magnetic radiation, they are the same phenomenon.

Well, I meant to turn on electromagnet, which will push off permanent magnet, so both of them will gain momentum. Part of the energy in form of the current will be consumed. If we use the same energy to produce a light beam, to give us some momentum, the momentum gained will be far smaller than the one gained by electromagnet, using the same energy. This does not make sense to me, because you are telling me that light is the most efficient thing to throw off. So how is that possible?

Yes, same with the conservation of energy.

You cannot run around either conservation law. All you can do is understand them and use them to accomplish your design goal. TANSTAAFL

Does it mean that conservation of momentum would not work in not closed system? Is it enough to put energy to the system, to make it not closed?

 

[Dale]

Does it mean that conservation of momentum would not work in not closed system?

Yes.

Is it enough to put energy to the system, to make it not closed?

Any external force makes the system non-isolated. It does not have to "put energy". For example, the energy to accelerate an automobile comes from the gasoline, not the road, but it is the force of the road that makes the car a non-isolated system whose momentum can change. If the car were in space its momentum could not change regardless of how much gasoline its engine used.

 

[Klockan3]

Well, I meant to turn on electromagnet, which will push off permanent magnet, so both of them will gain momentum. Part of the energy in form of the current will be consumed. If we use the same energy to produce a light beam, to give us some momentum, the momentum gained will be far smaller than the one gained by electromagnet, using the same energy. This does not make sense to me, because you are telling me that light is the most efficient thing to throw off. So how is that possible?

You forget to include the energy contained in the permanent magnet, since all mass you shoot away basically means you wasted E=mc^2 energy.

You can think like this for simplicity's sake, there are 2 kinds of particles in the world; Particles which move and particles which stands still. Both are made up of energy. Photons are made up of just particles that move, and resting mass are made up of just particles which stand still, while moving mass are a mix between moving particles and particles which stand still.

Now these particles can interact with each other, irl its a lot more complex but you can say that if you add two particles moving in the opposite direction together you can get an immobile particle, in the same way you can split an immobile particle into two moving which moves in opposite directions.

Anyway, everything you shoot away from your spaceship means that you must split immobile particles into moving, giving you one which moves in positive direction with the ship, this one you want to keep, then you also gets one moving in the other direction, this is the one we leave behind. Now, pure light is to just send that moving particle away, anything else you are also dumping a lot of immobile particles with that moving one and thus wasting a ton of extra energy.

Due to this spaceship fuel should ideally go in an as fast velocity as possible since then you use the least amount of immobile per mobile, nothing else really matters since energy is energy and no type of transforming energy is more powerful than anything else.

And yes a closed system is not closed if you add energy, since energy and momentum are really the same thing.

 

[Tominator]

Thanks for your explanations guys. I have not ever taught about it this way.

Any external force makes the system non-isolated. It does not have to "put energy". For example, the energy to accelerate an automobile comes from the gasoline, not the road, but it is the force of the road that makes the car a non-isolated system whose momentum can change. If the car were in space its momentum could not change regardless of how much gasoline its engine used.

So generally, momentum is always conserved. But what if we use, what Klockan3 has said

And yes a closed system is not closed if you add energy, since energy and momentum are really the same thing.

Lets consider a system with moving magnet and stationary coil. If light-weight magnet approaches heavy coil, a current will be induced in the coil. Part of the momentum of the magnet will be given to those charged particles. Current can be considered a form of energy as well as moving charged particles. So if we charge an acumulator by these charged particles, law of conservation of energy will be conserved. On the other hand momentum of the system will not be conserved.
How much of the momentum can be transformed to electric energy this way?
If we put current to a coil, to push off a magnet, would the coil gain the same momentum as the magnet?

 

[Dale]

On the other hand momentum of the system will not be conserved.

The momentum of the system (including the fields) will be conserved.

 

[Tominator]

The momentum of the system (including the fields) will be conserved.

Since, according to Klockan3, the energy and momentum is the same thing, wouldn't it be direct voiolation of conservation of energy, if we could draw off energy from the system, and also conserve momentum?
On the other hand, if we want to use it for space propulsion purposes, it does not metter, the only thing that matters is that the momentum of magnet and coil (not considering fields) would not conserve.
How big could the change in momentum of the coil and magnet system be (not considering the fields)?

 

[Dale]

Did you read the link on 4-momentum that I posted earlier?

 

[Tominator]

Did you read the link on 4-momentum that I posted earlier?

Well, I have clicked on the link, but those patterns scared me off. After your latest post, I have tried to read it again, but I did not understand it well.
From what I understood, the example was about subatomic particles, and it was mentioned there that "it is useful in relativistic calculations", so I do not see a connection to the case described previously. Coil or magnet can not gain the invariant mass, because they can not be considered particles. Or does it apply also on objects which are moving nowhere near the speed of light?
On the other hand, if the accumulator is charged by induced current, the system will become not closed, meaning that momentum does not have to be conserved.

 

[Dale]

Momentum is conserved for both subatomic particles and larger systems. It applies at all velocities. Anyway, the point is that, as Klockan3 and I have said energy is momentum in the time direction. Momentum is a vector quantity, so its conservation means that each component is individually conserved.

Here is a brief example for your scenario. Let's say that your vehicle (including fuel and payload) masses 10 metric tons (10000 kg). At rest, that corresponds to a four-momentum of (2998,0,0,0) GNs. If you convert 10 kg of fuel completely to light and throw it in the -x direction then that is a four-momentum of (3,-3,0,0) GNs. So by conservation of the four-momentum we know that the four-momentum of the remaining vehicle fuel and payload is (2995,3,0,0) GNs, which is a speed of 300 km/s.

 

[Tominator]

Here is a brief example for your scenario. Let's say that your vehicle (including fuel and payload) masses 10 metric tons (10000 kg). At rest, that corresponds to a four-momentum of (2998,0,0,0) GNs. If you convert 10 kg of fuel completely to light and throw it in the -x direction then that is a four-momentum of (3,-3,0,0) GNs. So by conservation of the four-momentum we know that the four-momentum of the remaining vehicle fuel and payload is (2995,3,0,0) GNs, which is a speed of 300 km/s.

Wow, that is a speed. The only bad thing about it is that our technology is not there yet.

Momentum is conserved for both subatomic particles and larger systems. It applies at all velocities. Anyway, the point is that, as Klockan3 and I have said energy is momentum in the time direction. Momentum is a vector quantity, so its conservation means that each component is individually conserved.

That is far more better explanation, than on wikipedia. But I still do not understand the post nr.75 :

The momentum of the system (including the fields) will be conserved.

Did you mean the EM wave, generated when EM field is formed arround the coil, and the electrical field of condensator=accumulator?
But then, if I understand the 4-momentum correctly, the change in mechanical momentum of the system would have to be equal to the momentum of the EM wave.

 

[Dale]

Did you mean the EM wave, generated when EM field is formed arround the coil, and the electrical field of condensator=accumulator?
But then, if I understand the 4-momentum correctly, the change in mechanical momentum of the system would have to be equal to the momentum of the EM wave.

The change of the momentum of the vehicle will be equal and opposite to the momentum of the EM wave so that the total momentum of the system (vehicle + EM) is conserved.

 

[Tominator]

The change of the momentum of the vehicle will be equal and opposite to the momentum of the EM wave so that the total momentum of the system (vehicle + EM) is conserved.

You have already told me that. This time I was not asking the same question again. The post nr. 75 of yours, which I did not understand well, referred to the post nr.74.
In this post I asked about momentum of a system composed of a coil and magnet, in which magnet is approaching the coil.

 

[Phrak]

The radius of the Earth is 46 Hz, but who's counting.

 

[Dale]

You have already told me that. This time I was not asking the same question again. The post nr. 75 of yours, which I did not understand well, referred to the post nr.74.
In this post I asked about momentum of a system composed of a coil and magnet, in which magnet is approaching the coil.

OK Tominator, get a blackboard and write 100 times: "Momentum is conserved for any isolated system". The details of the system are irrelevant.

 

[Tominator]

OK Tominator, get a blackboard and write 100 times: "Momentum is conserved for any isolated system". The details of the system are irrelevant.

I have already understood that. I have not said it is not conserved, only in the post 74 but that was because I considered the system not closed. But when you introduced me the
4-momentum, I realized it should be conserved, even thoug I previously taught it is not closed system. But I was not sure, so I wrote this:

Did you mean the EM wave, generated when EM field is formed arround the coil, and the electrical field of condensator=accumulator?
But then, if I understand the 4-momentum correctly, the change in mechanical momentum of the system would have to be equal to the momentum of the EM wave.

I was only asking how is the momentum conserved, not wheather it is conserved or not.
On the other hand it still seems to me weird that if I turn the momentum in closed system to energy, the momentum will stay conserved.

 

[Dale]

OK, I think I understand the question now. You don't "turn momentum to energy". Energy already is momentum in the time direction. So it is not a question of converting one into the other at all. Remember, the conservation of a vector quantity means that each component is independently conserved.

If I still missed the question perhaps you can rephrase.

 

[Tominator]

You have cleared that one up for me, thanks.
Although, there are some cases, where I really do not know, how is the momentum conserved there. For example:
There is a ship and atom. The ship exerts a strong force, in tiniest fraction of a second, on the atom. Assuming, the atom is able to accelerate that fast, it will be as if the ship bounced of a wall, wouldn't it? Because the atom can not go faster than light, there is a light speed "wall".
The Faster the bounc off, the stronger the inertial effect. So at some point, even if I bounce off a ball, it will be as if I bounced off a wall.
Well, momentum is always conserved, so I am not certain wheather are my assumptions with the wall and ball correct.

 

[Dale]

Let's say that the ship masses 10,000 kg and is traveling at 300 km/s, so it has a momentum of 3E6 kg km/s. Let's say the atom is a really heavy one like uranium, it masses 4E-25 kg, and let's say it is traveling at -300 km/s, so it has a momentum of -1E-22 kg km/s. By conservation of momentum after they collide the ship's momentum is still 3E6 kg km/s (to 28 digits of precision) so it is still traveling at 300 km/s.

So conservation of momentum does not imply that it is "as if the ship bounced off a wall".

 

[Tominator]

Thanks for answer, on the other hand we probably would not need to care about the momentum of the sip, because there will be no ship left.
But what if the ship and atom do not colide but the ship applies force on the atom to push it off and thus gain momentum. Since the weight of atom is small, the change in its momentum is enormous, even with several N of force. If I am correct, than energy used for longer period of time to create lower force, is equal to energy used to create massive force in a fraction of a second.
The Faster the bounce off, the stronger the inertial effect. So at some point, even if I bounce off a ball, it will be as if I bounced off a wall.
If big force is applied on the atom in a split of a second, the change in momentum of the atom (p=mv) would be tremendous and it would happen in a split of a second. The atom can not accelerate beyond the speed of light, so for the ship, it will be as if it bounced of a wall. Correct?

 

[Dale]

I still don't get your "wall" comments. Perhaps you can work out a concrete example.

Btw, relativistic momentum is a non-linear function of velocity: p=mv/sqrt(1-v²/c²) which increases without bound as the velocity approaches c.